Load the BirthdataNC into R and use kable to create a table with mean and sd by gender.
BirthdataNC <- read.csv("BirthdataNC.csv",
stringsAsFactor = FALSE)
kable(BirthdataNC %>%
group_by(gender) %>%
summarise(avweight = mean(weight), sdweight = sd(weight)), col.names = c("Gender", "Average Weight","Sd Weight"), digits=3)| Gender | Average Weight | Sd Weight |
|---|---|---|
| female | 6.903 | 1.476 |
| male | 7.302 | 1.517 |
Make an interactive histogram of weight by gender that also contains density plots in it. Add a vertical line with the average weight
# Interactive histogram of the data with density function included. The range goes from 0 to 12 by 0.3
p<-ggplot(BirthdataNC, aes(x=weight, fill=gender)) +
geom_histogram(aes(y=..density..),breaks=seq(0, 12, by = 0.3)) +
geom_vline(xintercept = 7.3, linetype="dotted", color = "darkgreen", size=1.7)+
geom_density(alpha=0.4)
ggplotly(p)# You could also add these two layers to plot normal distributios too, similar to what we did in class for the sampling dist. No need to that here, but this is how you do it.
# stat_function(fun = dnorm, args = list(mean = 6.9, sd = 1.47), col=2)+ stat_function(fun = dnorm, args = list(mean = 7.3, sd = 1.51), col=4)+ labs(title="Histogram for sample means")+ theme_classic()# Create quartiles of the data
quantile(BirthdataNC$weight)
# Create quartiles by gender.
female<-BirthdataNC %>%
filter(gender=="female")
female_quantile<-quantile(female$weight)
female_quantile
male<- BirthdataNC%>%
filter(gender=="male")
male_quantile<-quantile(male$weight)
male_quantile
# Create deciles of the data
# this creates a sequence from 0 to 1 by 0.1
deciles<-seq(0,1, by=0.1)
quantile(female$weight, deciles)
quantile(male$weight, deciles)
p75m<-quantile(male$weight, 0.75)
p45f<-quantile(female$weight, 0.45)
p75m<-
print(paste("Weight for 75th percentile for the whole population", p75m))
p45f<-
print(paste("Weight for 45th percentile for female population", p45f))## 0% 25% 50% 75% 100%
## 1.00 6.38 7.31 8.06 11.75
## 0% 25% 50% 75% 100%
## 1.00 6.25 7.13 7.75 11.63
## 0% 25% 50% 75% 100%
## 1.38 6.56 7.44 8.31 11.75
## 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%
## 1.000 5.392 6.000 6.500 6.866 7.130 7.380 7.630 7.940 8.380
## 100%
## 11.630
## 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%
## 1.380 5.476 6.310 6.866 7.190 7.440 7.810 8.130 8.488 8.964
## 100%
## 11.750
## [1] "Weight for 75th percentile for the whole population 8.31"
## [1] "Weight for 45th percentile for female population 7"What can you say about the distribution by looking at these graphs. Here you have to use another geometric that also ilustrates the distribution of your data. geom_violin() Explain what this graphs does.
# Boxplot by gender, interactive, figure out how to flip the coordinates
# Violin by gender, interactive, figure out how to flip the coordinates.
p2<-ggplot(BirthdataNC, aes(x=gender, y=weight, color = gender)) +
geom_boxplot() +
coord_flip()+
ggtitle("Weight distribution by gender - Boxplot")+
theme_classic()
ggplotly(p2)Using the normal distribution and the t-student find the critical values for \(\alpha=10% and 1%\)
# The value of alpha is use for Hypothesis testing
# Critical values for given alpha using the normal approximation and the t-student with 1000 d.f:
p2<-ggplot(BirthdataNC, aes(x=gender, y=weight, color = gender)) +
geom_violin(aes(fill = factor(gender))) +
ggtitle("Weight distribution by gender - Violin Plot")+
theme_classic()
ggplotly(p2)# Using the normal distribution and the t-studnet find the critical values for α=10
alpha <- c(0.10, 0.01)
# Critical values for given alpha using the normal approximation and the t-student with 1000 d.f:
n<-qnorm(alpha) # critical value for the normal distribution
n1<-round(qnorm(1-alpha), 3)
t<-round(qt(1-alpha, 1000), 3)
kable(data.frame(alpha, t , n1), digits=3, padding=5L, col.names = c("$\\alpha$", "T-student","Normal-right"))| \(\alpha\) | T-student | Normal-right |
|---|---|---|
| 0.10 | 1.282 | 1.282 |
| 0.01 | 2.330 | 2.326 |